The first rule of a secret society? Do not talk about the secret society. But a bunch of ad men were never likely to stay shtoom and so news of the Duke and Duchess of Cambridge's appearance at The Thirty Club was splashed all over the papers yesterday. Still, by the standards of advertising gurus, the members of this mysterious club have been remarkably discreet: their shadowy organisation was eclipsed by the glamour – and tattoos – of the couple who were the real stars of the gathering: Gary and Danielle Lineker. So what is The Thirty Club and how is it so powerful that it can attract footballing/wag royalty?

Rather prosaically, the group takes its name from the 30 founder members who established their private get-togethers in 1905 "for the betterment of advertising". That does not fool us. The more banal the group's stated purpose or the more boring the name – notorious secret coven The Bilderberg Group takes its name from a Dutch hotel where this gang of financiers and politicians first met in 1954 – the more suspicious we get. And The Thirty Club never takes minutes of its monthly dinners in Claridges' ballroom which, according to the Daily Mail, attract the media's big beasts, including Michael Grade, Lord Puttnam and Andrew Neil.

A spokesman for Prince William sounded slightly defensive when he explained that other senior royals suggested it would be an "interesting" event for him to attend. The ruling elite must realise that secret clubs are not a good look in an era of growing fears that we are governed by an oligarchy that may or may not have coalesced around the Bullingdon Club. Societies like these suffer a particularly bad press thanks to the internet, where every blameless group of drunken students, from Yale's Skull and Bones, famously joined by George W Bush, to Oxford University's Piers Gaveston Society, become a bunch of shape-shifting universe-ruling reptiles (author David Icke's famous conspiracy theory).

The Duke and Duchess of Cambridge's appearance has done nothing to allay my fears that The Thirty Club is secretly controlling my mind via the medium of lavish dinners. Thankfully, the presence of Gary and Danielle Lineker has.